The only place I found a good explanation of this issue is in The Writer’s Digest Grammar Desk Reference (by Gary Lutz & Diane Stevenson, Writers Digest Books, 2005, pp. 194/95 Chapter 16 “Two Special Problems with That”). Here are a few excerpts from that chapter (I’ve done the correct omissions in blue):
16A Omission of that from the Start of a Nominative Dependent Clause
Do not omit the indefinite relative pronoun that from the beginning of a nominative dependent clause if the subject of the clause is likely to be misread as the direct object of a transitive verb in the clause immediately preceding. Despite the widespread notion that that is a superfluous and discardable word, the inclusion of that often improves the readability of the sentence.
Consider this sentence: When a researcher discovers a new strain of flu could threaten a large segment of the population, the ethics panel determines whether the public should be notified immediately. Readers can initially misconstrue strain as the direct object of discovers. Only when they read the helping verb could will they realize that they have misread the sentence. The inclusion of that between discovers and a will ensure that readers can traverse the sentence without stumbling. . . .
Corrective additions to the following sentences have been boldfaced and bracketed.
- Mr. Green noticed [that] the kids he continued to bring to practice with him improved greatly.
- But on board his flight to Los Angeles, he found [that] the promised seat-back TVs were missing, and the bottled water ran out halfway there.
- I think it [the movie] should be required viewing for every American, but as usual, I fear [that] the people who could learn the most from the issues it raises will avoid it like a fund-raiser for free abortions.
The indefinite relative pronoun that can usually be omitted following verbs such as say, think, and hope, because there is no possibility of misreading: She said the food was overcooked. I thought the girl looked pale. He hopes the incumbent wins the election.
If two or more nominative dependent clauses follow a transitive verb, be sure to phrase the clauses in parallel form. . . .
Faulty: I realized I was going to be late for the meeting and that there was nothing I could do.
Correct: I realized that I was going to be late for the meeting and that there was nothing I could do.
Correct: I realized that I was going to be late for the meeting and there was nothing I could do.
In this revision, the first that is implicitly carried forward to the start of the second dependent clause, and the absence of a comma before and signals to the reader that what follows is another dependent clause and not a second independent clause.
16B Erroneous Doubled that
Writers sometimes mistakenly insert that at both ends of a dependent clause: He knows that if he oversleeps again that he might lose his job. The second that is superfluous and ungrammatical. A comma should be inserted in its place.
In each of the two following sentences, the second, bracketed that should be replaced by a comma.
- The PA Department of Revenue knows that no matter how careful a taxpayer is about reporting their income on the Personal Income Tax return [that] mistakes and oversights can happen.
- Many think that when they enter a highway from an on ramp [that] the approaching right lane traffic is required to move to the left lane in order to allow them to enter the traffic flow without interruption.
In the second sentence of the following excerpt, the third, bracketed that must be deleted, and it would be advisable to insert then in its place.
- Valentine’s Day is this weekend; if you are alone, it is your fault. So embrace your responsibility, feel that pain, and consider that if you are without a companion at 35—when you still have a fairly decent body—[that] when you die at 80, there will certainly be no one at your beside.
In researching this topic, I learned some new concepts, which will help me be more aware of this issue. I hope this helps you, too.
Have a great weekend! See you on Monday.